Disclaimer: these are not original ideas but are largely based on Sean Carroll’s “From Eternity to Here,” which I highly recommend.
You may have wondered why time seems to move forward and not backwards. Then, of course, you may have wondered what exactly one means by this. In other articles I’ve adopted a more philosophical approach; today I will focus on the physics.
There are several clues that tell us there is a fundamental difference between past and present. For example, we can only remember the past, not the future. We see glasses breaking, but never re-assembling themselves before our very eyes. When we put blue coloring in water and we stir, the coloring dissolves in the water. No matter how long we keep stirring, the two will never separate again.
This would make one think there is something in the laws of physics that differentiates between past and present. Alas, this is not the case (for physicists out there: it depends on how you define “time reversal” and I’m using CPT as a synonym of time-reversal symmetry.) The laws of physics are time-symmetrical. They predict exactly the same in both directions of time.
Let’s see what we mean by this. Imagine I film a pool game, disregarding the players and focusing on the balls themselves. The laws being time-symmetrical means I have no way to tell, upon watching the video, whether it is being played forward or backwards. Both chains of events are compatible with the laws of physics. If I do the same with any interaction between subatomic particles, I will get exactly the same result.
Some astute reader may have been thinking: “you’re wrong! There is a well-established law which is not time-symmetrical: the second law of thermodynamics.” If you don’t know what this is, here’s a brief summary. The second law of thermodynamics states that there is a quantity, called “entropy,” that increases in every isolated process. This gives us an arrow of time: the future is the direction in which entropy increases. There! Done.
Not so fast! Unfortunately, the laws of thermodynamics are not fundamental laws. They are actually consequences of the basic laws of nature (quantum mechanics or Newtonian mechanics, whatever tickles your fancy) together with probability theory. They are a prediction of our time-symmetrical laws, not an independent entity.
But how can something time-symmetrical predict something that is not time-symmetrical? The short answer is it can’t. The only way to achieve this result is to cheat.
But first, an aside on entropy, which is the most important concept we will deal with in this article. Entropy is usually explained to laypeople as a measure of how disorderly a system is. I will try to go a little beyond this simplistic view and give a more realistic account that’s actually in line with the math.
Entropy is (related to) the number of ways you can microscopically arrange a system without changing its macroscopic properties. For example, take a room full of air: if I swap one molecule in the top right by another one in the top left, there will be no appreciable difference in the air’s properties: it will have the same pressure, volume and temperature. In this case, a change in the microstate (the position and velocities of each molecule) has absolutely no effect on the macrostate (pressure, volume and temperature).
Each macrostate (set of properties visible with our “naked eye”) is compatible with a certain number of microstates. That is: for each pressure, volume and temperature combination there is a certain set of microscopic configurations that will give us this result. Entropy is defined as the (logarithm of) the number of microstates compatible with the current macrostate. That is, suppose I want to know the entropy of a gas at a certain temperature, pressure and volume: its entropy is the sum of all the possible microscopic combinations that give rise to the observed properties.
If we understand this, it is easy to derive the second law that says that entropy always increases. In fact, all the second law says is that systems tend to be in their more likely state, basically because it’s, well, more likely. But what does the number of microstates have to do with likelihood? A lot, in fact. Imagine a system (a gas in a container) that can be in one of three macroscopic states. For each macrostate, there is a certain number of microstates compatible with it: 1 for the first one, 10 for the second one and 100,000 for the third one. What are the odds of the system being in the third state? 100,000 / 100,011 or 99.98% (the compatible microstates divided by all the possible microstates). As you can see, the third system is the likeliest and is also the one with the highest entropy. Higher entropy equals higher probability.
So we’ve cracked it, haven’t we? Systems tend to evolve to likelier states (duh!) which means higher entropy, which means we will always see an increase from lower to higher entropy, which gives us an arrow of time. Right?
Wrong. Because this argument, which works from past to future, should also work from future to past. If I have some state at this moment, logic also dictates that its evolution towards the past increase its entropy, not decrease it! We should see an increase of entropy in both directions from the present, because the laws of physics are time-symmetrical. So, as I said before, our only way of deriving the time-asymmetrical second law is to cheat: entropy will always increase towards the future, as long as entropy in the past was very low. The question now is finding out why on Earth entropy was so low in the past, when it should have been high. We are right where we started!
Not quite, though. Because now we have transformed our original question (“why does time move forward?”) into “why was entropy so low in the past?” which is a lot more specific. If we manage to answer that, we will have finally cracked the mystery that has had the best minds in the planet scratching their heads for centuries.
So, ready for the solution?
Hah! Who said there’s a solution? Unfortunately, this has not been resolved yet. There are several promising lines of inquiry that I may go into some other day, but for the moment nothing is settled. In short: we have some wild guesses but really no idea. Feel free to contribute!
Who said that science claims to know everything?